How significant it is to know a structure of a substance at a spatial resolution as high as an atom can be identified, is obvious from atomic scale structure elucidations of DNA, carbon nanotube, and the like as well as subsequent developments. A diffraction pattern of X-rays or electron beams has an important role in the structure elucidations. In fields dealing with structures of atomic scale, it has been a general common sense that a phenomenon of diffraction has relevance only to crystals having periodicity. However, the common sense is greatly changing as a result of emergence of a new method called “diffraction microscopy” or “diffractive imaging”. See NPL 1.
As shown in FIG. 1, the diffraction microscopy is an imaging method for obtaining a real image by numerical calculation using a computer based on a diffraction pattern measured by experiment, and the diffraction microscopy can be referred to as a “digital lens” that realizes a function of a physical lens by digital calculation. The diffraction microscopy does not require a lens for image formation, and in principle, imaging at diffraction limit resolution can also be realized for a non-crystalline substance without periodicity, although the diffraction microscopy is based on the diffraction pattern. The diffraction microscopy can be generally applied to any substance with the wavy nature and can be applied to electrons with de Broglie wavelength. In recent years, the diffraction microscopy has significantly drawn attention, and advanced studies are globally progressed. See NPLs 2 to 4.
Basics of the diffraction microscopy are provided by NPLs 5 and 6.
FIG. 2 is a diagram showing a basic algorithm of the diffraction microscopy. In FIG. 2, f denotes an object, and F denotes what is obtained by applying Fourier transform FT{f} to object f. In FIG. 2, f and F are complex functions and corresponding amplitudes and phases are |f| and |F| as well as φ and Φ, respectively. The physical quantity generally obtained by diffraction experiment is only the diffraction intensity, i.e. amplitude, and the phase cannot be obtained. If the phase could be obtained by any kind of method, the object can be obtained by inverse Fourier transform. Therefore, “Fourier iterative phase retrieval” for obtaining the phase is proposed in NPLs 5 and 6. As shown in FIG. 2, the Fourier iterative phase retrieval is a method of applying respective constraints both in a real space and a reciprocal space (frequency area), i.e. “object constraint” and “Fourier constraint” (amplitude obtained by diffraction experiment), and sequentially and alternately repeating the Fourier transform and the inverse Fourier transform to obtain the phase. It is experimentally verified in NPL 7 that this method can provide an image of the object. The method of providing the object constraint varies depending on a specific algorithm.
FIG. 1 shows an example of simulation of the diffraction microscopy. The diffraction pattern on the left side is used as the Fourier constraint, and the object constraints are a real function, non-negativity and setting an area (support) surrounding a target to zero. An update algorithm called HIO (Hybrid Input-Output) is applied up to 5000 iterations, and an update algorithm called ER (Error Reduction) is applied after that and up to 10000 iterations. In this way, the real image on the right side is obtained. Although the diffraction pattern is created based on the real image because this is a simulation, the original real image is accurately reconfigured.